Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of D3×D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×D3×D9 |
| unambiguous semidirect product | (C3×D9)⋊C23 |
| unambiguous semidirect product | (D3×C9)⋊C23 |
| unambiguous semidirect product | (C3⋊D9)⋊C23 |
| Fitting | C22×C3×C9 ⋊ C22 |
| derived, Sylow | C3×C9 ⋊ C24 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | D3×D9 |
| commutator, cosocle, hypocenter | C3×C9 | C24 |
| Frattini | C3 | C22×D32 |
| Fitting | C22×C3×C9 | C22 |
| socle | C22×C32 | C2×D3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C22 | |
434 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 4 generators on 16 points:
(1,2)(3,4)(5,6,7)(9,11)(10,14)(12,15)(13,16);(6,7)(8,13,11,10,15,12,14,9,16);(3,4);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | D9×(C2×D3)⋊C4, D3×(C2×D9)⋊C4, #11721048, … |
| maximal normal subgroup of | D9×(C2×D3)⋊C4, D3×(C2×D9)⋊C4, #11721048, … |
| maximal quotient of | C2×D9×Dic6, C2×#88634, #11722458, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 544);